E1:
PROP. 5. There
cannot exist in the universe two or more
substances
having the same nature or
attribute.

Proof.--If several distinct
substances be granted, they must be distinguished one
from the other, either by the difference of their
attributes,
or by the difference of their
modifications
(E1P4). If only by the difference
of their attributes, it will be granted that there cannot
be more than one with an identical attribute. If by the
difference of their modifications--as
substance is
naturally prior to its modifications (E1P1),--it follows that setting
the modifications aside,
and considering substance in
itself, that is truly, (E1D3
and E1A6), there cannot be
conceived one substance
different from another,--that is
(by E1P4), there cannot be
granted several substances, but one
substance only.
Q.E.D.

Proof.--It is impossible that there
should be in the universe two
substances with an
identical attribute
[E1P5], i.e. which
have anything common to
them both (E1P2), and,
therefore (E1P3), one cannot
be the cause of another, neither can one be produced by
the other. Q.E.D.

E1:
PROP. 6, Corollary.--Hence it follows that a
substance cannot be
produced by anything external to itself.

Proof.-- For in the
universe nothing is granted, save
substances and their
modifications
(as appears from E1A1
and E1D3 and E1D5). Now (by E1P6) substance
cannot be produced by another substance, therefore it cannot be
produced by anything external to itself. Q.E.D. This is
shown still more readily by the absurdity of the
contradictory. For, if substance be produced by an
external cause, the knowledge of it would depend on the
knowledge of its cause (E1A4),
and (by E1D3) it would itself
not be substance.

Proof.--There can only be one
substance with an identical
attribute [E1P5], and
existence
follows from its nature (E1P7);
its nature, therefore, involves existence, either as
finite or infinite. It does not exist as
finite, for
(by E1D2) it would then be limited by
something else of the same kind, which would also
necessarily exist (E1P7); and
there would be two substances
with an identical
attribute,
which is absurd (E1P5).
It therefore exists as
infinite. Q.E.D.

E1:
PROP. 8, Note 2.--No
doubt it will be difficult for those who think about
things loosely, and have not been accustomed to know them
by their primary causes, to comprehend the demonstration
of E1P7: for such persons make
no distinction between the
modifications of substances
and the substances
themselves, and are ignorant of the
manner in which things are produced; hence they attribute
to substances the beginning which they observe in natural
objects. Those who are ignorant of true causes, make
complete confusion--think that trees might talk just as
well as men--that men might be formed from stones as well
as from seed; and imagine that any form might be changed
into any other. So, also, those who confuse the two
natures, divine and human, readily attribute human
passions to the deity, especially so long as they do not
know how passions
originate in the mind.
But, if people
would consider the nature of
substance, they would have
no doubt
about the truth of E1P7.
In fact, this proposition would be a universal axiom, and
accounted a truism. For, by
substance, would be
understood that which is in itself, and is conceived
through itself--that is, something of which the
conception requires not the conception of anything else;
whereas modifications
exist in something external to
themselves, and a conception of them is formed by means
of a conception of the thing in which they exist.
Therefore, we may have true
ideas of non-existent
modifications;
for, although they may have no actual
existence apart from the conceiving
intellect, yet their
essence
is so involved in something external to
themselves that they may through it be conceived. Whereas
the only truth substances
can have, external to the
intellect,
must consist in their
existence, because they
are conceived through themselves.
Therefore, for a person
to say that he has a
clear and distinct
--that is, a
true--idea of a substance,
but that he is not sure
whether such substance exists, would be the same as if he
said that he had a true idea, but was not sure whether or
not it was false (a little consideration will make this
plain); or if anyone affirmed that
substance is created,
it would be the same as saying that a
false idea was
true-- in short, the height of absurdity. It must, then,
necessarily be admitted that the
existence of
substance
as its essence is an
eternal truth.
And we can hence
conclude by another process of reasoning--that there is
but one such substance.
I think that this may profitably
be done at once; and, in order to proceed regularly with
the demonstration, we must premise:--
1. The true
definition
of a thing neither involves nor expresses
anything beyond the nature of the thing, defined. From
this it follows that--
2. No definition
implies or expresses a certain number of
individuals, inasmuch as it expresses nothing beyond the
nature of the thing defined. For instance, the definition
of a triangle expresses nothing beyond the actual nature
of a triangle: it does not imply any fixed number of
triangles.
3. There is necessarily for each individual existent
thing a cause why it should exist.
4. This cause of existence must either be contained in
the nature and
definition
of the thing defined, or must
be postulated apart from such definition.
It therefore follows
that, if a given number of
individual things
exist in nature, there must be some
cause for the existence of exactly that number, neither
more nor less.
For example, if twenty men exist in the
universe (for simplicity's sake, I will suppose them
existing simultaneously, and to have had no
predecessors), and we want to account for the existence
of these twenty men, it will not be enough to show the
cause of human existence in general; we must also show
why there are exactly twenty men, neither more nor less:
for a cause must be assigned for the existence of each
individual. Now this cause cannot be contained in the
actual nature of man, for the true definition of man does
not involve any consideration of the number twenty.
Consequently, the cause for the existence of these twenty
men, and, consequently, of each of them, must necessarily
be sought externally to each individual.
Hence we may lay
down the absolute rule, that everything which may consist
of several individuals must have an external cause. And,
as it has been shown already that
existence appertains to
the nature of substance,
existence must necessarily be
included in its definition;
and from its definition alone
existence
must be deducible. But from its definition (as
we have shown, Notes 2., 3.), we cannot infer the
existence of several substances; therefore it follows
that there is only one substance of the same nature.
Q.E.D.

E1:
PROP. 10, Note.-- It is
thus evident that, though two
attributes are, in fact,
conceived as distinct--that is, one without the help of
the other--yet we cannot, therefore, conclude that they
constitute two entities, or two different
substances. For
it is the nature of substance that each of its
attributes
is conceived through itself, inasmuch as all the
attributes it has have always existed simultaneously in
it, and none could be produced by any other; but each
expresses the reality or being of
substance.
It is, then,
far from an absurdity to ascribe several
attributes to
one substance: for nothing in nature is more clear than
that each and every entity must be conceived under some
attribute, and that its reality or being is in proportion
to the number of its attributes
expressing necessity or
eternity and infinity.
Consequently it is abundantly
clear, that an absolutely
infinite
being must necessarily
be defined [E1D6]
as consisting in infinite
attributes, each of
which expresses a certain eternal and infinite essence.
If
anyone now ask, by what sign shall he be able to
distinguish different substances, let him read the
following propositions, which show that there is but one
substance
in the universe, and that it is absolutely
infinite,
wherefore such a sign would be sought for in vain.

Proof.--If this be denied,
conceive, if possible, that God does not exist: then
[E1A7] his
essence
does not involve existence. But this (by E1P7) is absurd. Therefore God
necessarily exists.

Another Proof.--Of
everything whatsoever a cause or
reason must be assigned, either for its existence, or for
its non-existence--e.g. if a triangle exist, a reason or
cause must be granted for its existence; if, on the
contrary, it does not exist, a cause must also be
granted, which prevents it from existing, or annuls its
existence. This reason or cause must either be contained
in the nature of the thing in question, or be external to
it. For instance, the reason for the non-existence of a
square circle is indicated in its nature, namely, because
it would involve a contradiction. On the other hand, the
existence of
substance
follows also solely from its
nature, inasmuch as its nature involves
existence. (See E1P7)
But the reason for the
existence of a triangle or a circle does not follow from
the nature of those figures, but from the order of
universal nature in extension. From the latter it must
follow, either that a triangle necessarily exists, or
that it is impossible that it should exist. So much is
self-evident. It follows therefrom that a thing
necessarily exists, if no cause or reason be granted
which prevents its existence.
If, then, no cause or
reason can be given, which prevents the
existence of God,
or which destroys his existence, we must certainly
conclude that he necessarily does exist. If such a reason
or cause should be given, it must either be drawn from
the very nature of God, or be external to him -- that is,
drawn from another substance
of another nature. For if it
were of the same nature, God, by that very fact would be
admitted to exist. But substance
of another nature could
have nothing in common with God (by E1P2),
and therefore would be
unable either to cause or to destroy his existence.
As, then, a reason or cause
which would annul the divine
existence
cannot be drawn from anything external to the
divine nature, such cause must perforce, if God does not
exist, be drawn from God's own nature, which would
involve a contradiction. To make such an
affirmation
about a being absolutely
infinite
and supremely perfect,
is absurd; therefore, neither in the nature of God, nor
externally to his nature, can a cause or reason be
assigned which would annul his existence. Therefore, God
necessarily exists. Q.E.D.

Another Proof.--The
potentiality of non-existence is
a negation
of power, and contrariwise the potentiality of
existence is a power, as is obvious. If, then, that which
necessarily exists is nothing but finite beings, such
finite beings are more powerful than a being absolutely
infinite,
which is obviously absurd; therefore, either
nothing exists, or else a being absolutely infinite
necessarily exists also. Now we exist either in
ourselves, or in something else which necessarily exists
(see E1A1 and E1P7). Therefore a being
absolutely infinite
--in other words, God (E1D6)
--necessarily exists.
Q.E.D.

E1:
PROP. 11, Note.-- In
this last proof, I have purposely shown
God's existence a
posteriori, so that the proof might be more easily
followed, not because, from the same premises,
God's existence
does not follow a priori. For, as the
potentiality of existence is a power, it follows that, in
proportion as reality increases in the nature of a thing,
so also will it increase its strength for existence.
Therefore a being absolutely
infinite, such as God, has
from himself an absolutely infinite power of existence,
and hence he does absolutely exist.
Perhaps there will be
many who will be unable to see the force of this proof,
inasmuch as they are accustomed only to consider those
things which flow from external causes. Of such things,
they see that those which quickly come to pass--that is,
quickly come into existence--quickly also disappear;
whereas they regard as more difficult of
accomplishment--that is, not so easily brought into
existence --those things which they conceive as more
complicated.
However, to do away with this misconception,
I need not here show the measure of truth in the proverb,
"What comes quickly, goes quickly," nor discuss
whether, from the point of view of universal nature, all
things are equally easy, or otherwise: I need only
remark, that I am not here speaking of things, which come
to pass through causes external to themselves, but only
of substances which (by E1P6)
cannot be produced by any external cause.
Things which
are produced by external causes, whether they consist of
many parts or few, owe whatsoever perfection or reality
they possess solely to the efficacy of their external
cause, and therefore their existence arises solely from
the perfection of their external cause, not from their
own. Contrariwise, whatsoever perfection is possessed by
substance
is due to no external cause; wherefore the
existence of substance must arise solely from its own
nature, which is nothing else but its
essence.
Thus, the
perfection of a thing does not annul its existence, but,
on the contrary, asserts it. Imperfection, on the other
hand, does annul it; therefore we cannot be more
certain
of the existence of anything, than of the existence of a
being absolutely infinite
or perfect --that is, of God.
For inasmuch as his essence
excludes all imperfection,
and involves absolute perfection, all cause for
doubt
concerning his existence is done away, and the utmost
certainty
on the question is given. This, I think, will
be evident to every moderately attentive reader.